Decoupling in harmonic analysis and the Vinogradov mean value theorem

Joint IAS/Princeton University Number Theory Seminar
Topic:Decoupling in harmonic analysis and the Vinogradov mean value theorem
Speaker:Jean Bourgain
Affiliation:IBM von Neumann Professor; School of Mathematics
Date:Thursday, December 17
Time/Room:5:30pm - 6:30pm/S-101
Video Link:https://video.ias.edu/puias/2015/1217-Bourgain

Based on a new decoupling inequality for curves in $\mathbb R^d$, we obtain the essentially optimal form of Vinogradov's mean value theorem in all dimensions (the case $d = 3$ is due to T. Wooley). Various consequences will be mentioned and we will also indicate the main elements in the proof (joint work with C. Demeter and L. Guth).